Total curvature and rearrangements.

Artikel i vetenskaplig tidskrift, 2005

We study to what extent rearrangements preserve the integrability properties of higher order derivatives. It is well known that the second order derivatives of the rearrangement of a smooth function are not necessarily inL 1. We obtain a substitute for this fact. This is done by showing that the total curvature for the graph of the rearrangement of a function is bounded by the total curvature for the graph of the function itself.